The Samoa-born centre had not played since October 2014 due to a groin injury but the 24-year-old was named on the bench shortly before kickoff on Saturday and came on after 52 minutes at Welford Road.
England coach Eddie Jones is set to announce his first elite squad on Wednesday after taking over from Stuart Lancaster following the host nation's dismal 2015 World Cup campaign.
"Manu will keep improving but the start of the Six Nations is unrealistic because we need to make sure he is 100 percent right," Cockerill told the BBC.
"As soon as he's fit and good to go, he can go and play for England and do what he does but at this point he's Leicester's player, we've looked after him for a long time to get him fit, and I'm not going to push him through to play test matches now."
England used Brad Barritt, Sam Burgess, Jonathan Joseph, Henry Slade and Owen Farrell as centres during the disappointing World Cup campaign in which they failed to reach the knockout stages after Pool A defeats against Wales and Australia.
The powerful Tuilagi won the last of his 25 caps for England in June 2014 and played one test for the British and Irish Lions on the 2013 tour of Australia.
However, his career has been dogged by controversy and he was not considered for last year's World Cup after admitting assaulting two female police officers in April 2015.
He was also fined 3,000 pounds ($4,354.80) by England management for jumping into Auckland harbour from a ferry in the aftermath of the 2011 World Cup in New Zealand.
England have other injury concerns after wing Jonny May was ruled out of the entire Six Nations tournament because of a knee injury, while Bath forward Dave Attwood and Leicester lock Ed Slater will also miss the competition.
Slade, who broke his leg in December, will also be unavailable for the tournament, which England begin against Scotland at Murrayfield on Feb. 6.
(Reporting by Rob Hodgetts; Editing by John O'Brien)
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